This application is to study how sensory-motor transformations are accomplished in the cerebral cortex. In particular we will examine how spatial information is represented in cortex (Aim 1) and how coordinate transformations are accomplished between these representations (Aim 2). Previous work on these topics has examined how space is represented for achieving the movement of a single effector, for instance the eyes or the hand. However, movements generally involve multiple effectors and typically include hand-eye and bimanual movements. In Aim 1 we will advance a new finding, made in dorsal premotor cortex (PMd) during the last grant period, of a relative coding of the position of the hand, eyes and goal of a reach. This aim will test several new aspects and implications of relative coding. (1) It will examine the extent of relative coding in other areas of the sensorimotor pathway including area 5 and primary motor cortex. {2) It will determine if the 2 limbs also show a relative coding in cortical areas involved in reaching. Such a result would indicate that relative coding may be general mechanism for movements involving multiple body parts. (3) It will examine if relative coding of the hand is state dependent in PMd, and changes depending on the task, or if it is "hard wired". (4) It will determine if eye movement areas also show a relative coding of the eye and hand for eye movement tasks, which made facilitate eye- hand coordination. (5) It will directly test the hypothesis that relative coding, by its nature, is translation (and perhaps rotation) invariant across the workspace. In Aim 2 we will examine the gain field mechanism that is thought to be responsible for coordinate transformations between representations. (1) This aim will determine if gain fields exist simultaneously with relative position encoding. (2) It will determine whether gain fields in particular areas of cortex are concerned with extrinsic space around the body or intrinsic space within the body. 3) The mathematical mechanism for gain modulation will be determined. We will distinguish whether it is a pure multiplication of inputs or a function which approximates multiplication such as non-linear addition. Since gain fields are believed to be a general mechanism for neural computation, the results of these studies should have broad applicability to understanding neural processing beyond coordinate transformations. The results of the proposed studies can be used to help design therapies for patients suffering from damage to frontal and parietal cortex from strokes and traumatic brain injuries. They will help in understanding deficits that result from neurological diseases that effect cortical functioning, and can guide the diagnoses and treatments for these diseases.